A. Field of the Invention
The invention relates to puzzles, especially to map puzzles. In particular, it comprises a map puzzle formed from a planar map projection having a plurality of separable pieces which fit together in a variety of periodic, tesselated configurations, each enclosable within a frame specifically configured to that configuration, to illustrate specific features associated with the respective configurations.
B. Prior Art
Map puzzles are frequently used for entertainment purposes, as well as for instruction. Their utility for the latter purpose, however, is usually limited, since a given puzzle commonly can be assembled in only a single configuration. Further, the common map projections, while reasonably useful for many geopolitical purposes, contain significant distortions with respect to land sizes and locations that arise from the particular projection technique that is utilized.
Spherical surfaces such as maps of the earth's suface have commonly been projected onto two-dimensional (planar) surfaces by a variety of projective techniques. One common projective technique is that of projection from a point located at the earth's center onto a cylindrical surface that is positioned tangent to the earth at a selected point, usually the equator. This form of projection, known as "cylindrical central projection," distorts both parallels of latitude and parallels of longitude.
A modified form of this projection introduces a controlled distortion of the distance between parallels of latitude with increasing distance from the equator to maintain a conformal relationship in the projection (that is, lines of latitude remain parallel to lines of longitude, and the shape of small areas is preserved), but does so at the expense of distorting the size of areas on the map, particularly as one departs from the equator. Nonetheless, this map is commonly used, particularly for geopolitical maps, and is known as the Mercator projection. Other, less commonly used projections include stereographic projections (the spherical surface of the earth is projected onto a plane tangent to the earth at the given point); conic projections (projections onto conical surfaces); and polyhedral projections (projections onto polyhedral surfaces). With respect to the latter, the work of Schwartz has shown that a conformal projection onto an equilateral tetrahedron has a number of advantages in preserving conformality, as well as relative sizes.